{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Writing Fluid Simulations in Φ<sub>Flow</sub>\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/docs/Fluid_Simulation.ipynb)\n",
    "\n",
    "There are two main viewpoints for simulating fluids:\n",
    "\n",
    "* *Eulerian* simulations use grids, tracking fluid distribution and fluid velocity at fixed sample points\n",
    "* *Lagrangian* simulations track particles that move with the fluid.\n",
    "\n",
    "Φ<sub>Flow</sub> supports both methods to some extent but mainly focuses on Eulerian simulations.\n",
    "\n",
    "Before we discuss the various operations required for fluid simulations, let's define our variables and initial state.\n",
    "In this case, we will create a 64×96 grid, sampling velocity vectors [in staggered form](Staggered_Grids.html) and marker values at the centroids."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from tqdm.notebook import trange\n",
    "from phi.jax.flow import *  # imports sub-modules + core classes\n",
    "\n",
    "velocity = StaggeredGrid(Noise(), 'periodic', x=64, y=96)\n",
    "plot({\"velocity\": velocity, \"vorticity\": field.curl(velocity)})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Operator Splitting\n",
    "\n",
    "The Navier-Stokes equations for fluids, $\\frac{\\partial u}{\\partial t} = - (u \\cdot \\nabla) u - \\nu \\nabla^2 u - \\frac 1 \\rho \\nabla p + g$, comprise multiple terms.\n",
    "\n",
    "Operator splitting enables writing fast and stable fluid simulations by sequentially evaluating the different terms.\n",
    "For each of the terms, Φ<sub>Flow</sub> provides functions to compute them:\n",
    "\n",
    "* Advection: [`advect.semi_lagrangian`](https://tum-pbs.github.io/PhiFlow/phi/physics/advect.html#phi.physics.advect.semi_lagrangian) \\[Stam 1999\\], [`advect.mac_cormack`](https://tum-pbs.github.io/PhiFlow/phi/physics/advect.html#phi.physics.advect.mac_cormack) \\[MacCormack 2002\\]\n",
    "* Diffusion: [`diffuse.explicit`](https://tum-pbs.github.io/PhiFlow/phi/physics/diffuse.html#phi.physics.diffuse.explicit), [`diffuse.implicit`](https://tum-pbs.github.io/PhiFlow/phi/physics/diffuse.html#phi.physics.diffuse.implicit)\n",
    "* Pressure projection: [`fluid.make_incompressible`](https://tum-pbs.github.io/PhiFlow/phi/physics/fluid.html#phi.physics.fluid.make_incompressible) \\[Chorin and Temam 1968\\]\n",
    "\n",
    "All of these functions take in a state variable and return the new state after a certain time `dt` has passed.\n",
    "In the following example, the velocity is self-advected and made incompressible, while the marker is passively advected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "@jit_compile\n",
    "def operator_split_step(v, p, dt, viscosity=0.1):\n",
    "    v = advect.semi_lagrangian(v, v, dt)  # velocity self-advection\n",
    "    v = diffuse.explicit(v, viscosity, dt)\n",
    "    v, p = fluid.make_incompressible(v, (), Solve(x0=p, rank_deficiency=0))\n",
    "    return v, p\n",
    "\n",
    "velocity0, pressure0 = fluid.make_incompressible(velocity)\n",
    "velocity1, pressure1 = operator_split_step(velocity0, None, dt=1.)\n",
    "plot({'initial vorticity': field.curl(velocity0), 'after step': field.curl(velocity1)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x360 with 4 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "@jit_compile\n",
    "def operator_split_step(v, p, dt):\n",
    "    v = advect.semi_lagrangian(v, v, dt)  # velocity self-advection\n",
    "    v = diffuse.explicit(v, 0.1, dt)\n",
    "    v, p = fluid.make_incompressible(v, (), Solve(x0=p, rank_deficiency=0))\n",
    "    return v, p\n",
    "\n",
    "velocity0, pressure0 = fluid.make_incompressible(velocity)\n",
    "velocity1, pressure1 = operator_split_step(velocity0, None, dt=1.)\n",
    "plot({'initial vorticity': field.curl(velocity0), 'after step': field.curl(velocity1)})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "We can use [`iterate`](https://tum-pbs.github.io/PhiML/phiml/math/index.html#phiml.math.iterate) to compute a trajectory by repeatedly calling `operator_split_step`.\n",
    "All intermediate states are stacked along the specified dimension which we call `time`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b3eed64f46114c2783a2b1b885f88036",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/100 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "velocity_trj, pressure_trj = iterate(operator_split_step, batch(time=100), velocity0, pressure0, dt=1., range=trange)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Alternatively, we could have written a `for` loop, added all intermediate states to a list, and stacked the results afterward.\n",
    "Now, let's plot this trajectory by animating the `time` dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video width=\"864\" height=\"360\" controls autoplay loop>\n",
       "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAIGZ0eXBNNFYgAAACAE00ViBpc29taXNvMmF2YzEAAAAIZnJlZQACRDhtZGF0AAACrwYF//+r\n",
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       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x278718bb460>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(field.curl(velocity_trj), animate='time', same_scale=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Higher-Order Simulations\n",
    "\n",
    "The operator splitting approach is not compatible with more accurate numerical schemes.\n",
    "For more accurate simulations, we can use higher-order spatial schemes as well as time integration.\n",
    "In that case, we define a momentum equation which computes the PDE terms directly, without integrating them in time.\n",
    "The following example computes explicit fourth-order accurate advection and diffusion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def momentum_equation(v, viscosity=0.1):\n",
    "    advection = advect.finite_difference(v, v, order=4, implicit=None)\n",
    "    diffusion = diffuse.finite_difference(v, viscosity, order=4, implicit=None)\n",
    "    return advection + diffusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Next, we perform time integration with the incompressibility constraint.\n",
    "This is considerably more expensive than the previous approach but yields much more accurate results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "is_executing": true,
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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       "model_id": "84d6be3681f44556b14be7ad30213c27",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/200 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x2787591ecd0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@jit_compile\n",
    "def rk4_step(v, p, dt):\n",
    "    return fluid.incompressible_rk4(momentum_equation, v, p, dt, pressure_order=4)\n",
    "\n",
    "velocity = CenteredGrid(Noise(vector='x,y'), 'periodic', x=64, y=96)\n",
    "velocity0, pressure0 = fluid.make_incompressible(velocity, order=4)\n",
    "velocity_trj, pressure_trj = iterate(rk4_step, batch(time=100), velocity0, pressure0, dt=.5, substeps=2, range=trange)\n",
    "plot(field.curl(velocity_trj), animate='time', same_scale=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Further Reading\n",
    "\n",
    "The [Kolmogorov flow notebebook](prerendered/HigherOrder_Demo.ipynb) shows higher-order fluid flow with forcing.\n",
    "\n",
    "For a comparison of various schemes in both accuracy and performance is given [here](prerendered/Taylor_Green_Comparison.ipynb).\n",
    "\n",
    "Coupling between centered and staggered fields can be seen in the [smoke plume notebook](https://tum-pbs.github.io/PhiFlow/Fluids_Tutorial.html) and [Python script](https://github.com/tum-pbs/PhiFlow/blob/master/demos/smoke_plume.py)."
   ]
  }
 ],
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